東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Elliptic carleman estimates and appl...

Le Rousseau, Jerome.

Linked to FindBook

Google Book

Amazon

博客來

Elliptic carleman estimates and applications to stabilization and controllability.. Volume I,. Dirichlet boundary conditions on Euclidean space

Record Type:	Electronic resources : Monograph/item
Title/Author:	Elliptic carleman estimates and applications to stabilization and controllability./ by Jerome Le Rousseau, Gilles Lebeau, Luc Robbiano.
remainder title:	Dirichlet boundary conditions on Euclidean space
Author:	Le Rousseau, Jerome.
other author:	Lebeau, Gilles.
Published:	Cham :Springer International Publishing : : 2022.,
Description:	viii, 411 p. :ill. (some col.), digital ;24 cm.
[NT 15003449]:	Introduction -- Part 1: Calculus with a Large Parameter, Carleman Estimates Derivation -- (Pseudo-)differential Operators with a Large Parameter -- Carleman Estimate for a Second-Order Elliptic Operator -- Optimality Aspects of Carleman Estimates -- Part 2: Applications of Carleman Estimates -- Unique Continuation -- Stabilization of the Wave Equation with an Inner Damping -- Controllability of Parabolic Equations -- Part 3: Background Material: Analysis and Evolution Equations -- A Short Review of Distribution Theory -- Invariance under Change of Variables -- Elliptic Operator with Dirichlet Data and Associated Semigroup -- Some Elements of Functional Analysis -- Some Elements of Semigroup Theory -- Bibliography -- Subject Index -- Index of Notation.
Contained By:	Springer Nature eBook
Subject:	Carleman theorem. -
Online resource:	https://doi.org/10.1007/978-3-030-88674-5
ISBN:	9783030886745

Elliptic carleman estimates and applications to stabilization and controllability.. Volume I,. Dirichlet boundary conditions on Euclidean space
Le Rousseau, Jerome.

Elliptic carleman estimates and applications to stabilization and controllability.Volume I,Dirichlet boundary conditions on Euclidean space[electronic resource] /Dirichlet boundary conditions on Euclidean spaceby Jerome Le Rousseau, Gilles Lebeau, Luc Robbiano. - Cham :Springer International Publishing :2022. - viii, 411 p. :ill. (some col.), digital ;24 cm. - Progress in nonlinear differential equations and their applications,v. 971421-1750 ;. - Progress in nonlinear differential equations and their applications ;v. 97..

Introduction -- Part 1: Calculus with a Large Parameter, Carleman Estimates Derivation -- (Pseudo-)differential Operators with a Large Parameter -- Carleman Estimate for a Second-Order Elliptic Operator -- Optimality Aspects of Carleman Estimates -- Part 2: Applications of Carleman Estimates -- Unique Continuation -- Stabilization of the Wave Equation with an Inner Damping -- Controllability of Parabolic Equations -- Part 3: Background Material: Analysis and Evolution Equations -- A Short Review of Distribution Theory -- Invariance under Change of Variables -- Elliptic Operator with Dirichlet Data and Associated Semigroup -- Some Elements of Functional Analysis -- Some Elements of Semigroup Theory -- Bibliography -- Subject Index -- Index of Notation.

This monograph explores applications of Carleman estimates in the study of stabilization and controllability properties of partial differential equations, including the stabilization property of the damped wave equation and the null-controllability of the heat equation. All analysis is performed in the case of open sets in the Euclidean space; a second volume will extend this treatment to Riemannian manifolds. The first three chapters illustrate the derivation of Carleman estimates using pseudo-differential calculus with a large parameter. Continuation issues are then addressed, followed by a proof of the logarithmic stabilization of the damped wave equation by means of two alternative proofs of the resolvent estimate for the generator of a damped wave semigroup. The authors then discuss null-controllability of the heat equation, its equivalence with observability, and how the spectral inequality allows one to either construct a control function or prove the observability inequality. The final part of the book is devoted to the exposition of some necessary background material: the theory of distributions, invariance under change of variables, elliptic operators with Dirichlet data and associated semigroup, and some elements from functional analysis and semigroup theory.

ISBN: 9783030886745

Standard No.: 10.1007/978-3-030-88674-5doiSubjects--Topical Terms:

3270405
Carleman theorem.

LC Class. No.: QA331 / .L4 2022

Dewey Class. No.: 515.9

Elliptic carleman estimates and applications to stabilization and controllability.. Volume I,. Dirichlet boundary conditions on Euclidean space
LDR:03335nmm a2200349 a 4500 001 2299149
003 DE-He213
005 20220328210219.0
006 m d
007 cr nn 008maaau
008 230324s2022 sz s 0 eng d
020 $a 9783030886745 $q (electronic bk.)
020 $a 9783030886738 $q (paper)
024 7 $a 10.1007/978-3-030-88674-5 $2 doi
035 $a 978-3-030-88674-5
040 $a GP $c GP
041 0 $a eng
050 4 $a QA331 $b .L4 2022
072 7 $a PBKJ $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBKJ $2 thema
082 0 4 $a 515.9 $2 23
090 $a QA331 $b .L617 2022
100 1 $a Le Rousseau, Jerome. $3 3596422
245 1 0 $a Elliptic carleman estimates and applications to stabilization and controllability. $n Volume I, $p Dirichlet boundary conditions on Euclidean space $h [electronic resource] / $c by Jerome Le Rousseau, Gilles Lebeau, Luc Robbiano.
246 3 0 $a Dirichlet boundary conditions on Euclidean space
260 $a Cham : $b Springer International Publishing : $b Imprint: Birkhauser, $c 2022.
300 $a viii, 411 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a Progress in nonlinear differential equations and their applications, $x 1421-1750 ; $v v. 97
505 0 $a Introduction -- Part 1: Calculus with a Large Parameter, Carleman Estimates Derivation -- (Pseudo-)differential Operators with a Large Parameter -- Carleman Estimate for a Second-Order Elliptic Operator -- Optimality Aspects of Carleman Estimates -- Part 2: Applications of Carleman Estimates -- Unique Continuation -- Stabilization of the Wave Equation with an Inner Damping -- Controllability of Parabolic Equations -- Part 3: Background Material: Analysis and Evolution Equations -- A Short Review of Distribution Theory -- Invariance under Change of Variables -- Elliptic Operator with Dirichlet Data and Associated Semigroup -- Some Elements of Functional Analysis -- Some Elements of Semigroup Theory -- Bibliography -- Subject Index -- Index of Notation.
520 $a This monograph explores applications of Carleman estimates in the study of stabilization and controllability properties of partial differential equations, including the stabilization property of the damped wave equation and the null-controllability of the heat equation. All analysis is performed in the case of open sets in the Euclidean space; a second volume will extend this treatment to Riemannian manifolds. The first three chapters illustrate the derivation of Carleman estimates using pseudo-differential calculus with a large parameter. Continuation issues are then addressed, followed by a proof of the logarithmic stabilization of the damped wave equation by means of two alternative proofs of the resolvent estimate for the generator of a damped wave semigroup. The authors then discuss null-controllability of the heat equation, its equivalence with observability, and how the spectral inequality allows one to either construct a control function or prove the observability inequality. The final part of the book is devoted to the exposition of some necessary background material: the theory of distributions, invariance under change of variables, elliptic operators with Dirichlet data and associated semigroup, and some elements from functional analysis and semigroup theory.
650 0 $a Carleman theorem. $3 3270405
650 0 $a Differential equations, Partial. $3 518115
650 1 4 $a Differential Equations. $3 907890
650 2 4 $a Systems Theory, Control. $3 893834
650 2 4 $a Operator Theory. $3 897311
650 2 4 $a Functional Analysis. $3 893943
700 1 $a Lebeau, Gilles. $3 716632
700 1 $a Robbiano, Luc. $3 3596423
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Progress in nonlinear differential equations and their applications ; $v v. 97. $3 3596424
856 4 0 $u https://doi.org/10.1007/978-3-030-88674-5
950 $a Mathematics and Statistics (SpringerNature-11649)